Quantum communications system having at least one waveplate to alter pulse polarization and associated methods

ABSTRACT

A quantum communications system may include a transmitter node, a receiver node, and a quantum communications channel coupling the transmitter node and receiver node. The transmitter node may include a pulse transmitter, a pulse divider downstream from the pulse transmitter, and at least one first waveplate upstream from the pulse divider and configured to alter a polarization state of pulses travelling therethrough. The receiver node may include at least one second waveplate being a conjugate of the at least one first waveplate, a pulse recombiner upstream from the at least one second waveplate, and a pulse receiver downstream from the at least one second waveplate.

FIELD OF THE INVENTION

The present invention relates to the field of communications, and, moreparticularly, to quantum communication systems and related methods.

BACKGROUND OF THE INVENTION

In a quantum communications system, sometimes referred to as a quantuminformation system, information is exchanged between a transmitter nodeand a receiver node using encoded single photons. Each photon carriesinformation that is encoded on a property of the photons, such as itspolarization, phase, or energy in time. These quantum communicationssystems generally require sending information from one node to anothernode, such as a transmitter node, usually referred to as “Alice,” and areceiver node, usually referred to as “Bob.” The term quantumcommunications system encompasses multiple applications. For example aquantum key distribution (QKD) system allows the sharing ofcryptographic keys between the transmitter node and receiver node, thusallowing a more secure communication between the two parties. A QKDsystem provides a test whether any part of the key would be known to anunauthorized third party eavesdropper, usually referred to as “Eve.”

Individual bits of the bit stream are transmitted using single photons.By using complementary properties to which Heisenberg's uncertaintyprinciple applies, information may be encoded into a photon to preventthe unauthorized third party, e.g., “Eve,” from monitoring the photonsince it would disturb its state. When a secret key is establishedbetween the two parties by this QKD system, the two parties may thenencrypt data transmitted over any conventional communications channel.

In the QKD system, the two parties as Alice and Bob at the respectivetransmitter node and receiver node may use two or more non-orthogonalbases to encode bit values. The laws of quantum mechanics apply to thephotons and any measurement of the photons by an eavesdropper, e.g.,Eve, without prior knowledge of the encoding basis of each photon,causes an unavoidable change to the state of some of the photons. Thesechanges to the states of the photons may cause errors in the bit valuessent between the transmitter node and receiver node, and by comparing apart of the common bit steam, the two parties may determine if theeavesdropper, e.g., Eve, has gained information. Photon polarization isoften used to provide the complementary properties for encoding, and isused in the common QKD protocol, BB84, and may be applied to conjugatestates, such as the polarization state of the quantum state. Other QKDprotocols, such as E91, may be based on entanglement of photon pairs andused in a QKD system.

Other applications of a quantum communications system include quantumrandom number generator (QRNG) systems that use the inherentindeterminacy of quantum entangled photons to produce random binarydigits, and quantum secure direct communication (QSDC) systems thattransfer direct information between Alice and Bob without a distributionkey. In QSDC systems, the transmitter node as Alice generates quantumphotons that carry secure quantum information representative of the datato be communicated. The quantum photons carrying the data are decodedupon receipt at the receiver node as Bob.

QSDC systems are based on quantum mechanics for direct transmission ofinformation without employing a distributed cryptographic key to encryptthe data. QSDC systems may be more efficient than some keyedcommunication systems because the cryptographic key development and keystorage requirements are eliminated. Transmitted photons carrying datawithin the QSDC system may be more readily maintained in confidencewithout being erased, manipulated or monitored by unintended thirdparties, such as Eve. These QSDC systems may provide tamper evidentcommunication links that are compatible with the direct transmission ofdata at the single photon level. As a result, QSDC systems may becomemore important as quantum computers increase in sophistication and allowconventional cryptographic keys to be more easily broken, while quantuminterconnects are developed that network computers together.Improvements in QSDC systems may also provide quantum signatures andimprove the efficiency and impart greater security in a quantumcommunications channel.

Existing telecommunications security approaches based on computationalkey management have security shortcomings that are threatened by“download today, decrypt tomorrow” quantum attacks. Quantumcommunications systems may be more secure than conventionalcommunications systems, but come at a cost of orders of magnitude slowerdata rates, resulting in a disconnect between security and speed.Physical layer security protocols have been proposed as potentialapproaches for quantum cryptography errors, but are limited by the speedof opto-mechanical components or interfering channel phenomena, makinginsertion into existing optical communication systems challenging.Analog attacks for physical layer security protocols, even those againstcomputational attacks, represent an additional threat that should beconsidered for new communication protocols.

Many QKD protocols exists, but none are considered to stand above theothers. State-of-the-art communications systems use many different QKDprotocols. A round-robin DPS (Differential Phase-Shift) quantum keyprotocol has a high QBER (quantum bit error rate) tolerance of about50%, but the best key rate is about 10 Kbit/s over 50 kilometers offiber. Continuous variable protocols face similar limitations, and theperformance, e.g., key rate or operability, degrades with channelconditions such as existing in free-space optical communications. RSA(Rivest-Shamir-Adleman) encryption on classical optical carriers cantheoretically be used to counter “download today and decrypt tomorrow,”but the possibility of quantum computers in the near future makes longterm personal information, such as bank information and social securitynumbers, vulnerable to attacks.

On the other hand, current physical layer security approaches mayprovide an analog layer of protection to communication systems and offeradvantages that address quantum cryptography errors. However, thesesystems often rely on reconfigurability of transceivers or theircommunications channels to achieve security. For example, the speeds ofopto-mechanical components or varying channel conditions may impactperformance. While these communication systems are secure, they mayoperate on orders of magnitude slower than required to facilitateinsertion into state-of-the-art optical communication systems.

SUMMARY OF THE INVENTION

In general, a quantum communications system may include a transmitternode, a receiver node, and a quantum communications channel coupling thetransmitter node and receiver node. The transmitter node may comprise apulse transmitter, a pulse divider downstream from the pulsetransmitter, and at least one first waveplate upstream from the pulsedivider and configured to alter a polarization state of pulsestravelling therethrough. The receiver node may comprise at least onesecond waveplate being a conjugate of the at least one first waveplate,a pulse recombiner upstream from the at least one second waveplate, anda pulse receiver downstream from the at least one second waveplate.

The pulse divider may be configured to divide each pulse having aplurality of X photons into a plurality of Y time bins with Y>X. Thepulse receiver may comprise at least one single photon detector.Additionally, the pulse divider may comprise a plurality of stagedbirefringent crystals. The pulse recombiner may also comprise aplurality of staged birefringent crystals.

The pulse transmitter may be configured to generate temporally modulatedphotons. The quantum communications system channel may comprise at leastone of a fiber optic communications channel, a free space opticcommunications channel, and an underwater optic communications channel.The pulse transmitter may be configured to generate orthogonallymodulated photons. The pulse transmitter may be configured to generate abit stream of quantum pulses in a quantum key distribution (QKD)protocol.

A method aspect is for operating a quantum communications systemcomprising a transmitter node, a receiver node, and a quantumcommunications channel coupling the transmitter node and receiver node.The method may include operating the transmitter node to generatequantum pulses at a pulse transmitter and dividing the quantum pulses ata pulse divider, the transmitter node also comprising at least one firstwaveplate upstream from the pulse divider to alter a polarization stateof pulses travelling therethrough. The method may also include operatingthe receiver node to recombine the divided quantum pulses at a pulserecombiner, and receiving the recombined pulses at a pulse receiver. Thereceiver node also may comprise at least one second waveplate downstreamof the pulse recombiner and being a conjugate of the at least one firstwaveplate.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention willbecome apparent from the detailed description of the invention whichfollows, when considered in light of the accompanying drawings in which:

FIG. 1 is a block diagram of the quantum communications system havingthe pulse divider that divides each pulse into time bins in accordancewith a non-limiting example.

FIG. 2 is a graph showing the data rate in GHz versus the link length inkilometers for different stages using the quantum communications systemof FIG. 1 .

FIG. 3 is a graph of normalized cross-correlation versus measured photonnumber and the quantum communications system of FIG. 1 compared to othercommunication systems.

FIG. 4 is a bar chart showing the impulse response along the quantumcommunications channel for an intruder (Snoopy) versus the receiver node(Bob).

FIG. 5 is a flowchart showing a method of operating the quantumcommunications system of FIG. 1 .

FIG. 6 is a block diagram of the quantum communications system similarto that shown in FIG. 1 , but incorporating at least one waveplate toalter pulse polarization.

FIG. 7 is schematic diagram showing pulse polarization over a spherethat depicts polarization using waveplates in the quantum communicationssystem of FIG. 6 .

FIG. 8 is a graph comparing the number of possible states versus thenumber of stages for the quantum communications systems shown in FIGS. 1and 6 .

FIG. 9 is a schematic block diagram showing the optical communicationssystem of FIG. 6 and the positioning of waveplates and error detectionat the receiver node.

FIG. 10 is a flowchart showing a method of operating the quantumcommunications system of FIG. 6 .

DETAILED DESCRIPTION

The present description is made with reference to the accompanyingdrawings, in which exemplary embodiments are shown. However, manydifferent embodiments may be used, and thus, the description should notbe construed as limited to the particular embodiments set forth herein.Rather, these embodiments are provided so that this disclosure will bethorough and complete. Like numbers refer to like elements throughout.

Referring initially to FIG. 1 , a quantum communications system isillustrated generally at 20 and may be operative as a quantum securedirect communications (QSDC) system, which permits direct communication,such as without use of a cryptographic key. The quantum communicationssystem 20 may also operate as a quantum key distribution (QKD)communications system that shares cryptographic keys between thetransmitter node 26 and receiver node 28 that may communicate with eachother via a quantum communications channel 30 or via a conventionalcommunications system 52 to exchange keys. The quantum communicationschannel 30 may be a free-space optical, underwater, and/or fiber opticcommunications channel.

This quantum communications system 20 includes its transmitter node 26referred to as Alice, its receiver node 28 referred to as Bob, and thequantum communications channel 30 coupling the transmitter node andreceiver node. The quantum communications system 20 may incorporatepulse division to place a quantum state into a super position of timebins. Neighboring quantum states thus experience interference with eachother, which scrambles the original communications data stream. Coupledwith the no-cloning theorem of quantum mechanics, this acts as aphysical layer of security that can be used to securely transmit quantumdata streams within the quantum communications channel 30 without theadditional use of a cryptographic key in some embodiments.

As illustrated, the transmitter node 26 includes a pulse transmitter 40and a pulse divider 42 downstream therefrom. The pulse divider 42 isconfigured to divide each pulse having a plurality of X photons into aplurality of Y time bins with Y is greater than X. The receiver node 28includes a pulse recombiner 54 and a pulse receiver downstream 56 fromthe pulse recombiner. In an example, the pulse transmitter 40 mayinclude a laser or similar pulse generator that generates a laser andmay include quantum pulses carrying communications data that may beencrypted and the pulses may be of varying length from continuous wave(CW) to very short pulses, and may be divided into bins. This pulsetransmitter 40 may also generate temporally modulated photons,orthogonally modulated photons, and in an example, other spatiallymodulated photons. The pulse transmitter 40 may also generate a bitstream of quantum pulses in a quantum key distribution (QKD) protocol.The pulse divider 42 may include a plurality of elements such as stagedbirefringent crystals 43 that divide each pulse having a plurality of Xphotons into the plurality of Y time bins where Y is greater than X. Thepulse recombiner 54 also may have staged birefringent crystals 55 thatreconstruct the photons received over the quantum communications channel30. The pulse division and recombining stages may be based on using freespace optics, such as a combination of polarizing beam splitting cubes,½ and ¼ waveplates, mirrors, and free space delay lines. Fibercomponents may be used such as polarization beam splitters and combinersin fiber based on separating and combining different spatial modes ofpolarizing beam fiber, with fiber delay lines, and manual or electronicfiber polarization controllers based on fiber birefringence, orfiber-free space polarization control-fiber where free spacepolarization control could include electronic or manual waveplates, or alithium niobate modulator, for example.

The transmitter node also includes a controller 48 that operates thepulse transmitter 40 and a transceiver 50 that connects to acommunications system 52 as will be explained in further detail belowand which may be part of the quantum communications channel 30. Thepulse receiver 56 may include an optical detector circuit 66 thatincorporates opto-electric (OE) circuitry such as a spatial filter andbeam splitter that splits signals into a phase basis or time basis usinga phase detector or photon detector. A single photon detector 74 maydetect single photons or the optical detector circuit 66 may detect aplurality of photons at one time. The receiver node 28 also includes acontroller 78 and transceiver 80 connected to the pulse receiver 56. Thetransceiver 80 is coupled to the communications system 52 andcommunicates with the transceiver 50 located at the transmitter node 26.

The pulse transmitter 40 and pulse divider 42 may be formed asconventional off-the-shelf optical components and the bit stream may bemodulated onto a laser transmitter or other optical pulse generatordevice that generates and transmits pulses as part of the pulsetransmitter 40. In an example, the output power of generated pulses maybe attenuated to a few hundred photon regime, such as above 100 photonsand fewer than 10,000 photons, such that high-speed optical detectors atthe pulse receiver 28 as part of the optical detector circuit 66 candetect even while using more conventional off-the-shelf (COTS) opticaldetector components. At the transmitter node 26, each of the X photondata bit pulses is divided into Y time bins with the pulse divider 42.For the case of Y greater than X, a few hundred to about ten thousandphoton bits are placed into a super position state, which is propagatedacross the quantum communications channel 30. Any measurements mademid-length by “Eve” as an intruder cannot be used to decode the originalbit stream, due to the wave function collapse of the individual photonsof the original bit upon measurement. This provides a quantum resourcefor security at the few hundred to about ten thousand photon level thatusually is constrained to a single photon in a bit of quantum resourcesecurity.

At the receiver node 28, photons are received and the receiver nodeoperates as a matched or conjugate-receiver and the photonsreconstructed at the pulse recombiner 54, which employs the stagedbirefringent crystals 55 to reconstruct the photons as a reverse of thedeconstruction process that has occurred at the transmitter node 26. Atamper evident port at the output of the receiver node 28 may flagcorrupted photons, indicating a compromise of the communications link.High speed, conventional off-the-shelf GHz class optical detectors atthe optical detector circuit 66 may be used to measure the recombinedbit stream, composed of a hundred to about ten thousand photons. Thisallows a quantum secured communications link to extend greater than 100kilometers, while maintaining Gbps data rates using these conventionaloff-the-shelf optical transmitter and receiver components at the pulsetransmitter 40, pulse divider 42, pulse recombiner 54, and pulsereceiver 56.

Referring now to FIG. 2 , the graph shows the data rate in gigahertz(GHz) versus the link length in kilometers relative to the differentnumber of stages, which are illustrated as the vertical lines, for ananticipated quantum secure rate-distance trade-off using the opticaldetector circuit 66 at the pulse receiver 56. The graph shows that aslong as the received photon number is greater than the minimum detectorsignal-to-noise ratio (SNR), the data rates do not exponentially reducewith distance similar to the way that single photon quantumcommunications systems perform.

Referring now to FIG. 3 , there is illustrated a graph of the normalizedcross-correlation relative to the measured photon number and showing theresults of the quantum communications system 20 of FIG. 1 referred to asthe “hybrid” compared to other communications such as a quantumcommunications system using a single photon polarization (referred to as“quantum”) and a “classical” or conventional optical communicationssystem. The graph shows the degree of correlation of a transmitted imageat different points such as Alice at the transmitter node 26, Snoopy orEve as the intruder at the mid-link connection of the quantumcommunications channel 30 and interfering to determine thecommunications data, and Bob at the receiver node 28. The communicationschannel 30 connects the transmitter node 26 and receiver node 28 thatincludes a 20-stage circuit for a matched transmitter node to thereceiver node as a function of the photon number.

The simulation is for communications data transmitted over a 100kilometer fiber link. In terms of the correlation, the NCC (NormalizedCross-Correlation) of 1 indicates a perfect correlation, while the NCCof 0 shows no correlation. For a quantum communications system using asingle photon instead of a plurality of photons as in the system 20 ofFIG. 1 , the NCC values for Snoopy or Eve at the midpoint of the quantumcommunications channel 30 are nearly 0. However, at the receiver node28, the NCC values are lower. This is due to photon annihilation fromthe fiber absorption that impacts the quality of image reconstructionand shows the expected limits of single photon channels. A classical orconventional optical communications system has millions or more photons,and the conventional implementations have adequate security with thistransceiver pair, but are more than 10 times higher than the hybrid(FIG. 1 ) in quantum cases. The hybrid case corresponding to the opticalcommunications system of FIG. 1 has 100 to 10,000 photons and themeasurement provides NCC values that are just barely above whiteGaussian noise for Snoopy or Eve, but which also reflect a near perfectreconstruction for the intended recipient at the receiver node 28,corresponding to Bob.

Due to the longer communications channel 30, the few hundred or thousandphoton system as shown by the block diagram of FIG. 1 out-performs botha single photon quantum communications system by beating the singlephoton rate-distance trade that degrades the image quality between Aliceand Bob as the respective transmitter node 26 and receiver node 28, andthe classically equivalent system of a conventional opticalcommunications system by reducing the information shared between Aliceand Snoopy (Eve) as the intruder by about 10 times in terms ofmaximizing information to the receiver node 28 as Bob, while minimizinginformation to the intruder such as Snoopy or Eve at the mid-point. Thehybrid case as shown in the graph of FIG. 3 and corresponding to thequantum communication system 20 of FIG. 1 shows the possibility of usinga different class of high-speed, low SWaP detectors and can beat thesingle photon rate-distance trade.

Referring now to FIG. 4 , a bar chart of the impulse response with power(NU) versus time in nanoseconds (ns) shows that the quantumcommunications system 20 behaves as expected. The left-hand bar chartfor Snoopy as the intruder (Eve) is compared to the performance from Bobas the receiver node 28 on the right. The impulse response changes foreach measurement for Snoopy or Eve due to the collapse of the superposition state of the impulse when X photons are placed into Y binswhere Y is greater than X. This can be leveraged to provide a layer ofsecurity. The impulse response remains constant at the receiver node 28for Bob, allowing Bob to directly measure what the transmitter node 26of Alice transmits.

The three communications systems shown in the graph of FIG. 3 includeadvantages and disadvantages. A quantum communications system using asingle photon requires a slow quantum detector. The system impulseresponse will change for repeated measurements, for example, with aquantum super position collapse and the pulse division scrambles thebits to provide high security, but the link loss degrades imagereconstruction. A classical or conventional optical communicationssystem without any quantum basis will have tens of thousands to millionsof photons per bit and may use a high-speed classical or conventionaloff-the-shelf detector, but has no quantum layer of security. The systemimpulse response is constant for repeated measurements and the pulsedivision scrambles the bits and the image may be reconstructed despitelink loss.

The quantum communications system 20 as described relative to FIG. 1 asa quantum-classical hybrid system has as few as a hundred photons toabout 10,000 photons per bit and may use a high-speed conventionaloff-the-shelf optical detector circuit 66. The system 20 includes aquantum layer of security where the system impulse response changes forrepeated measurements and a quantum super position collapse. The pulsedivision at the pulse divider 42 scrambles the bits as a classical layerof security and the image may be reconstructed despite link loss.

Referring now again to FIG. 1 , in an example, the pulse divider 42 andpulse recombiner 54 may operate to provide a divided pulse quantum keydistribution that may be applied on top of existing QKD protocols andimplemented downstream of the pulse transmitter 40 and upstream of thepulse receiver 56 to improve the performance of existing QKD protocols.It is possible that the transmitter node 26 may also be configured togenerate spatially modulated photons that are transmitted over amulti-mode optical fiber, as compared to temporally modulated photonsthat are communicated over a single mode optical fiber connection.Temporally or spatially modulated photons may use optical polarizationencoding, and in the single photon transmission, each photon may have atransmitted quantum basis. The transmitter node 26 and receiver node 28may communicate using the communications system 52, which may include aclassical communications channel and be formed as a fiber optic,free-space, wired, or other conventional communications channel. Thiscommunication system 52 may be employed for cryptographic keygeneration, quantum key distribution (QKD), or communication withnetwork devices using the conventional transceivers 50,80. The quantumcommunications system 20 may use cryptographic key sifting or operate asa QSDC system, and the quantum communications channel 30 may be integralwith the communication system 52 shown by the dashed lines connectingthe two, indicating that both quantum communications and non-quantumcommunications may be transmitted over any communications channel aspart of the communication system.

Reference is made to U.S. patent application Ser. No. 17/179,562entitled, “Quantum Communications System Using Pulse Divider andAssociated Methods,” and U.S. patent application Ser. No. 17/179,600entitled, “Communications System Using Pulse Divider and AssociatedMethods,” both applications which were filed on Feb. 19, 2021, thedisclosures which are hereby incorporated by reference in theirentirety. Those applications disclose use of either a single photonpulse transmitter or optical transmitter for generating a conventionalbit as tens of thousands of photons for single photon encoding anoptical transmitter for tens of thousands or more of photons per bit andthe pulse divider for a quantum communications system or opticalcommunications system. Components as described in those applications maybe modified and incorporated into the quantum communications system 20of FIG. 1 .

In an example, the optical pulse output from the pulse transmitter 40 atthe transmitter node 26 may be an output bit stream of photons that areencoded bit values. The photon polarization may provide a complementaryproperty used for encoding purposes, such as in the QKD protocol, BB84.Other protocols, such as the E91 protocol, may be used that includesencryption or the entanglement of photon pairs. Each bit of informationsuch as a “0” or “1” may be encoded onto an individual photon or groupof photons as in the quantum communications system 20 of FIG. 1 byselecting from a pair of orthogonal polarization states. In the BB84 QKDprotocol, two pairs of orthogonal states are used, and each pair oforthogonal states is referred to as a “basis.” The basis may providepolarization state pairs in a rectilinear basis having vertical andhorizontal polarization, such as 0° and 90°, and a diagonal basis havingopposite diagonal direction polarization, such as 45° and 135°.

It is also possible to use a circular basis of left-handedness andright-side handedness depending on what other bases are used that areconjugate to each other. The quantum communications system 20 may use anunencrypted non-quantum communications channel, such as thecommunications system 52, for the key exchange or key sifting process.It is possible to use a continuous-variable QKD (CV-QKD) protocol or adiscrete-variable (DV-QKD) protocol. Single photons may be generated forthe DV-QKD protocol, usually as optical pulses, and usually uses singlephoton detectors 74 at the receiver node 28, for example, as an array ofsingle photon optical detectors. In contrast to the DV-QKD protocol, theCV-QKD protocol may use conjugate-continuous degrees of freedom (fieldquadratures) of a light pulse prepared in a Gaussian (coherent orsqueezed) state to transmit signals that constitute a shared randomness.

At the receiver node 28, in some examples, the field quadratures of eachlight pulse may be measured using as an example, shot-noise limited,balanced homodyne or heterodyne detectors, such as phase detectors,which have an advantage of not requiring single photon detection andoperating at high GHz speed detection rates. In the CV-QKD protocol,often a local oscillator (OL) signal may be generated at the transmitternode 26 and the CV-QKD protocol may involve polarization encoding andmultiplexing techniques.

As noted before, the transceiver 50 at the transmitter node and thetransceiver 80 at the receiver node 28 may communicate with each othervia the communications system 52, which may be a conventional, i.e.,non-quantum communications system. For example, Bob as the receiver node28 may communicate with Alice as the transmitter node 26 over theconventional communications system 52, and transmit data regarding thebasis in photons that were received at the receiver node 28 when singlephoton polarization is used. The transmitter node 26, e.g., Alice, maytransmit data about the basis in which each photon was transmitted tothe receiver node 28, e.g., Bob, using the communications system 52. Anybits having a different basis may be discarded, leaving the remainingbits as the basis for a shared cryptographic key in the key verificationor key shifting phase. The subset of shared bits used by both parties,e.g., Alice and Bob at their respective transmitter node 26 and receivernode 28, may be used to check against eavesdropping by the unauthorizedparty, e.g., Eve, which would have introduced errors into thecommunications stream of bits.

The transmitter node 26 and its pulse transmitter 40 may include othercomponents not illustrated in detail, such as a spatial light modulator(SLM) that imposes a spatially varying modulation by modulatingintensity and phase, a waveguide array and associated optical circuitrythat generates phase bin states, and an attenuation filter that may beused with the large number of photons usually generated in aconventional off-the-shelf optical pulse transmitter to reduce thenumber of photons and operate as the “hybrid” quantum communicationssystem 20 shown in FIG. 1 .

As noted before, the transmitter node 26 includes the pulse transmitter40 for generating a bit stream of quantum optical pulses. The pulsetransmitter 40 may be a laser or other pulse generator circuits ofoptical pulses.

The optical pulses from the transmitter node 26 are an output bit streamof photons that have encoded bit values. The photons may be temporallyor spatially modulated and transmit a quantum basis that includes time,and in some examples, phase parameters, including optical polarizationencoding. A photon polarization may provide the complementary propertyused for encoding purposes. In the quantum communications system 20 ofFIG. 1 , optical pulses may be arranged in time bins and photonpolarization may be applied to conjugate states, such as phase encoding.The quantum communications system 20 may use entanglement of photonpairs, and each bit of information such as a “0” or “1” may be encodedonto an individual photon by selecting from a pair of orthogonalpolarization states. In the optical communications system of FIG. 1 ,the information may be encoded onto the group of photons.

In an example, two pairs of orthogonal states may be used, and each pairof orthogonal states may be referred to as a “basis.” The bases mayprovide polarization state pairs in a rectilinear basis having verticaland horizontal polarization, such as 0° and 90°, and a diagonal basishaving opposite diagonal direction polarization, such as 45° and 135°.It is also possible to use a circular basis of left-handedness andright-handedness depending on what other bases are used that areconjugate to each other.

The transmitter node 26 includes its controller 48 operatively connectedto the pulse transmitter 40 and other components at the transmitter node26 to control their operation. The controller 48 operates the pulsetransmitter to transmit one or more photons, such as 100 to 10,000photons, in a polarization state defined by the bit and basis and intime bins, and may record the time the bit and its photons weretransmitted. This process may be repeated for the string of bits as astream of photons. The transmitter node 26 may include its transceiver50 connected to the controller 48 and operative to communicate withconventional networked components via the communications system 52.Additional functions for Quantum Key Distribution (QKD) at the receivernode 28 may be provided via the communications system 52.

The transmitter node 26 may transmit the bit stream of pulses via thepulse divider 42 over the quantum communications channel 30, which maybe integral or separate from the communications system 52. The photonsmay be temporally modulated or spatially modulated depending on end useand the construction of the pulse transmitter 40. It is possible to usethe same communications channel 30 such as a fiber optic cable for bothquantum communications and conventional communications.

The receiver node 28 includes the pulse recombiner 54 that recombinesthe pulses, and pulse receiver 56, which in an example includesopto-electronic (OE) circuitry having an optical detector circuit 66that receives the bit stream of pulses from the transmitter node 26 overthe quantum communications channel 30 and had been reconstructed via thepulse recombiner 54. The optical detector circuit 66 may include aspatial filter, which may be used depending on the example oftransmitted pulses to split the optical signal into an optical phase oroptical time stream, allowing measurement in the phase basis or timebasis. A spatial filter may be used to “clean up” the bit stream ofoptical pulses and produce a smooth intensity profile as a cleanerGaussian signal that has unwanted multiple-order energy peaks removedsuch that the central maximum of a diffraction energy pattern. A spatialfilter may include a microscopic objective lens, a pinhole aperture anda positioning mechanism having precision X-Y movement at the center ofthe pinhole that operates as the focal point of the objective lens in anon-limiting example. A spatial filter may also be advantageous becauseit operates as a filter for any spatial probability distributionfunction that may not be characterized, cloned and reintroduced to thepublic portion of the quantum communications channel 30. Thus, anyspatial probability distribution disturbances that are introduced maynot cleanly exit the spatial filter, and thus, Bob at the receiver node28 may use this information as a metric to reveal tampering.

The optical detector circuit 66 may receive the bit stream of opticalpulses and detect the optical pulses and generate signals that may beprocessed at the controller 78, which may process and demodulate thesignals representative of the optical pulses depending on thecommunications protocol. At the receiver node 28, the optical detectorcircuit 66 may be formed as a single photon detector 74 for measuringphotons in the time basis and in respective time bins, where the opticalpulses are transmitted in respective time bins for data encoding. In anexample, the optical detector circuit 66 may include an array of singlephoton detectors 74. The optical detector circuit 66 may also include aphase detector circuit for measuring the photons in the phase basis.

The controller 78 at the receiver node 28 is connected to theconventional transceiver 80, which may communicate via the conventionalor non-quantum communications system 52 with other networked componentsor to the transceiver 50 located at the transmitter node 26. Thetransmitter node 26 may include other components not illustrated indetail, such as a spatial light modulator (SLM) that imposes a spatiallyvarying modulation by modulating intensity and phase, a waveguide arraythat increases bit generation and phase bin states, and an attenuationfilter, which operate together with other optical components to transmittemporally modulated photons or spatially modulated photons and performoptical polarization encoding.

It is possible to include a phase detector and the single photondetector 74 for phase basis and time basis measurements. Generally, aneigenstate |Ψ> as a photon of a particular basis may be prepared andtransmitted from the transmitter node 26 as Alice over the quantumcommunications channel 30 to the receiver node 28 as Bob. In aconventional QKD system, if the eigenstate |Ψ> was prepared in the samephoton basis that Eve or Bob as the receiver node 28 chooses to measurethe quantum state in, both will measure the same state that Alice at thetransmitter node 26 initially prepared. If Eve or Bob at the transmitternode 28 choose a different basis than the one Alice at the receiver node26 initially prepared the quantum state in, both would collapse theeigenstate m into one of the eigenstates of the basis they weremeasuring in, and would have a 50% chance in a d=2 data structure, forexample, corresponding to a random guess, of correctly identifying theassociated bit value of the state that Alice sent. This practicality maybe applied to the multiple photon quantum communications system 20 ofFIG. 1 .

This use of mutually unbiased bases, and the impact of preparing andmeasuring in inconsistent bases, may be used to establish a more securecommunications link between Alice as the transmitter node 26 and Bob asthe receiver node 28 over the quantum communications channel 30. As Eveis forced to annihilate the state Alice 26 had prepared in order to gainany information about it, and as Eve must randomly choose a basis tomeasure the state in, on average Eve will choose the wrong basis 50% ofthe time, both resulting in measurements which do not provide Eveinformation about the original state, and revealing Eve's presence toBob as the receiver node 28 downstream through a quantum bit error rate(QBER) that is higher than a certain threshold value.

It is generally assumed that the eigenstate prepared in a particularbasis, does not change as it propagates. Thus, If Eve, and Bob at thereceiver node 28, choose the same basis to measure the state that Aliceat the transmitter node 26 initially used to prepare the state in, Eveand Bob will both measure it accurately. For a 4-state transmission,however, Eve as an intruder has on average a 75% chance of correctlyretrieving the bit value that Alice as the transmitter node 26 sends, asshe has a 50% chance of correctly choosing the right basis and 100%accuracy of retrieving the associated bit value in the correct basis,and a 50% chance of choosing the wrong basis, and a 50% accuracy ofretrieving the associated bit value when measuring in the wrong basis.The amount of error that Bob as the receiver node 28 can tolerate beforeknowing that the quantum communications channel 30 is insecure and thatEve is present, is in part dependent on this probability, whichessentially reflects the amount of information that Eve has access to.

Increasing the maximum threshold of the quantum bit error rate (QBER)that Bob as the receiver node 28 can tolerate before concluding that thequantum communications channel 30 is insecure, may increase secure linklengths, increase secure bit rates, and enable more efficient and costeffective implementations of the quantum communications system 20 inexisting communication links. It may also better enable securecommunications for QKD systems. Additionally, the increased thresholdmay also secure the transmission of quantum information using the system20 in general, for example, for distributed quantum computing or sensingapplications.

The quantum communications system 20 increases the maximum QBERthreshold where an initial state |Ψ> has its temporal probabilitydistribution broadened, so that it interferes with other neighboringbits in the bit stream, and scrambles the state and bit stream in thepublic link of the quantum communications channel 30 that Eve has accessto. Any measurements made at a location other than where Alice at thetransmitter node 26 and Bob at the receiver node 28 are located willreduce the information available to Eve, even if Eve chooses to measure|Ψ> in the same basis that the state was initially prepared in. Thequantum communications system 20 even with multiple pulses may reduceEve's information about the eigenstate |Ψ> in the public segment of thequantum communications channel 30 even for measurements she conducts inthe correct basis. The QBER threshold required for unconditionalsecurity may be increased even when Eve as an intruder chooses the rightbasis. The probability that Eve will measure the state Alice at thetransmitter node 26 initially sent is reduced. As a result, using thequantum communications system 20 of FIG. 1 as a QSDC system, Alice asthe transmitter node 26 and Bob as the receiver node 28 may toleratehigher system losses, increase communication link distances, relaxoptical detector circuit 66 requirements, and more easily adapt thequantum communications system 20 into existing telecom networks.

Time basis measurements may be performed with direct detection toresolve the arrival times of pulses associated with the various bitvalues that Alice 26 sends. It is also possible to incorporate into thesystem 20 the time to frequency conversion techniques disclosed incommonly assigned U.S. patent application Ser. No. 16/583,346 filed Sep.26, 2019, entitled, “Quantum Communication System Having Time toFrequency Conversion and Associated Methods,” the disclosure which ishereby incorporated by reference in its entirety.

It is possible that phase basis measurements may be performed by passinga single photon state through a Mach-Zender interferometer, which has adelay set by a time bin width of a protocol for the quantumcommunications system 20 or a half width of a waveguide. Single photoninterference occurs in a central time window, which the two outputs of aMach-Zender interferometer may resolve constructively or destructivelydepending on the eigenstate of the phase basis that was sent. Forexample, if phase state 1 was sent with an associated bit value 0, aphase detector may yield a detection event for P1 on Detector 1, and nodetection event on P1 of Detector 2.

Different circuit examples of pulse dividers 42 and pulse recombiners 54may be incorporated into the quantum communications system 20 of FIG. 1. The pulse divider 42 may receive an input pulse of a first energylevel and divide the pulse into a sequence of temporally spacedlower-energy pulses. The pulse recombiner 54 may combine the temporallyspaced pulses for input into the pulse receiver 56. The pulse divider 42may be formed from a sequence of M birefringent elements, such as stagedbirefringent crystals 43, which divide an initial pulse into a sequenceof 2^(M) pulses. This sequence of pulses may include a first group ofpulses that have a first polarization, and a second group of pulses thathave a second orthogonal polarization. It is possible that the pulses inthe first and second groups are interleaved with one another, so thatthe sequence of pulses have alternating linear polarizations.

The birefringent elements may be formed from staged birefringentcrystals (43) 1, 2, . . . , N. Crystals 43 at odd-numbered positions inthe sequence may have their optic axes oriented at a 45-degree angle toa direction of linear polarization of the pulse, while crystals at theeven-numbered positions may be oriented in the same direction as thelinear polarization of the pulse, so that at each crystal, a pulse issplit into two equal-intensity pulses, one as an ordinary (o) wave pulseand a second as an extraordinary (e) wave pulse. The o and e pulses areseparated in time by Δt=|1/ν_(e)−1/ν_(o)|L, where ν_(o) and ν_(e) arethe group velocities of the o- and e-waves and L is the crystal length.The length of the shortest crystal in the cascade of crystals 43 may bechosen so that Δt exceeds the pulse duration. The length of the m^(th)crystal in the cascade may be L_(m)=2^(m-1)L₁ to produce equally spacedpulses. An example of the birefringent element or crystal 43 is Yttriumvanadate.

The pulse recombiner 54 may be formed from a second sequence ofbirefringent elements as staged birefringent crystals 55 in an example,which also may be formed from Yttrium vanadate. Any alternating pulseswith orthogonal polarizations may be separated with a polarizing beamsplitter, and counter-propagate through a gain medium that requires aspecific direction of linear polarization. A waveplate may exchange thedirection of polarization of the counter-propagating beams, ensuring thecorrect polarizations for the beam entering the gain medium, and reversethe pulse replicas before the replicas are recombined into a finaloutput pulse.

A mirror may be employed at the pulse recombiner 54 to rotate thepolarization of the divided pulses by 90 degrees before pulses are fullyrecombined so that all pulses experience the same total delay andrecombine into the output pulse. The pulse divider 42 and the pulserecombiner 54 may be implemented by a single stack of birefringentcrystals 43,55. For pulse division, a pulse may be passed in a firstdirection through a stack of birefringent crystals 43 and for pulserecombination, a sequence of pulses may be passed in a second, oppositedirection through a stack of birefringent crystals 55.

Examples of different pulse dividers 42 and pulse recombiners 54 thatmay be modified for use with the quantum communications system 20 ofFIG. 1 are disclosed in U.S. Pat. Nos. 8,456,736; 10,109,976; and10,374,376; and in the articles: Zhou et al., “Divided-PulseAmplification of Ultrashort Pulses,” Optics Letters, 32(7), 2007, pp.871-873; Zhang et al., “Divided Pulse Soliton Self-Frequency Shift: AMulti-Color, Dual-Polarization, Power-Scalable, Broadly Tunable OpticalSource,” Optics Letters, 42(3), 2017, pp. 502-505; and Lamb et al.,“Divided-Pulse Lasers,” Optics Letters, 39(9), 2014, pp. 2775-2777, allof the disclosures which are hereby incorporated by reference in theirentirety.

The use of the pulse dividers 42 and pulse recombiners 54 provides a lowprobability of detection where weak pulses are hid in tailored noise andmakes the probability of detection low. There is a low probability ofintercept because each bit, such as 100 photons to 10,000 photons foroperation in the system 20 of FIG. 1 , may be divided into many copiesand distributing each copy into bins provides a system 20 where nouseful information about the original message is gained. The system 20may be tamper evident because attempts to measure the data mid-link maybe detected by the intended recipient and it is compatible with existingmethods of data encryption with added potential for protecting againstthe attacks.

Referring now to FIG. 5 , there is illustrated generally at 100 aflowchart showing a method of operating the quantum communicationssystem 20 of FIG. 1 . The process starts (Block 102) and the transmitternode is operated to generate quantum pulses at a pulse transmitter 40(Block 104). The quantum pulses are divided at a pulse divider 42 todivide each pulse having a plurality of X photons into a plurality of Ytime bins with Y greater than X (Block 106). The receiver node 28 isoperated to recombine the quantum pulses at a pulse recombiner 54 (Block108). The recombined pulses are received at the pulse receiver 56 (Block110). The process ends (Block 112).

Referring now to FIG. 6 , there is illustrated a block diagram of aquantum communications system indicated generally at 200 having at leastone waveplate 284 to alter a pulse polarization. The reference numeralsfor components described in FIG. 6 that are common in function to thecomponents in the quantum communications system 20 of FIG. 1 are giventhe same reference numerals in the block diagram of FIG. 6 except thosereference numerals start in the 200 series of FIG. 6 .

As illustrated, the transmitter node 226 includes the pulse transmitter240 and pulse divider 242 downstream from the pulse transmitter and atleast one first waveplate 284 upstream from the pulse divider 242 andconfigured to alter a polarization state of pulses travelingtherethrough. The receiver node 228 also includes at least one secondwaveplate 288 that is a conjugate of the at least one first waveplate284. The pulse recombiner 254 is connected upstream from the at leastone second waveplate 288. The pulse receiver 256 is downstream of thepulse recombiner 254 and second waveplate 288, and may include theoptical detector circuit 266 that includes at least one single photondetector 274. The optical detector circuit 266 may detect photonsgreater than 100 photons and less than 10,000 photons as a non-limitingexample. The optical communications system 200 illustrated in FIG. 6provides security against analog attacks for physical layer securityprotocols.

A conjugate receiver system is formed as integral with the receiver node228 and provides an additional physical layer security against analogattacks via spread photon matched receivers and polarization diversity,which increases the complexity of the encoding. For example, for a15-stage quantum communications system 200, this provides a 2⁶⁰increasing complexity in time against a brute force analog attack. Thisquantum communications system 200 may create phase relations to spreadpulses that are matched in the conjugate receiver as a receiver node228, making it difficult for an eavesdropper to implement both a“download today, decrypt tomorrow” type of computational attack. Thematched transmitter node 226 and receiver node 228 may be reconfigurablewhile maintaining their scalability and their ability to providecommunications at high data rates. This allows the transmitter node 226as Alice and the receiver node 228 as Bob to share an analog key as towhat polarization setting to use in the quantum communications system200, thus updating the settings as required to maintain securecommunication.

As shown in FIG. 6 , the at least one first waveplate 284 is at thetransmitter node 226 and at least one second waveplate 288 is at thereceiver node 228. The quantum communications system 200 incorporates aconjugate receiver node 228 that provides an additional physical layerof security against analog attacks as compared to the quantumcommunications system 20 described in FIG. 1 using polarizationdiversity, which greatly increases the complexity of the encoding. Forexample, a 15 stage system may provide about a 2⁶⁰ increase incomplexity to a brute force analog attack. Phase relations may becreated in the spread pulse that are matched at the receiver node 228,making it difficult for an eavesdropper to implement both a “downloadtoday, decrypt tomorrow” type of computational attack and a real timeanalog attack.

The matched transmitter node 226 and receiver node 228 may bereconfigurable while maintaining their scalability and ability toprovide communications at high data speeds. This allows Alice as thetransmitter node 226 and Bob as the receiver node 228 to share an analogkey as to what polarization settings to use at their respective nodes,updating their settings as needed to maintain secure communication. Thequantum communications system 200 is applicable to free space, space,underwater, and/or fiber communication links, and complementsflipped-basis QKD and QSDC by providing similar performance advantageswith a simpler implementation that uses linear optics, allowing foroperation in free-space optical links. It may use COTS components, e.g.,beam splitters, waveplates, and mirrors.

In an example, the bit stream is modulated onto the pulse transmitter240. The output power may be modified and amplified for “classical”transmission by attenuating to X photons that permits high speedclassical optical detectors to detect, but where X<Y as aclassical/quantum hybrid. In some examples, it may be possible toattenuate to a single photon quantum regime. Photons are received at thematched receiver node 228 and reconstructed in reverse of thedeconstruction process. A tamper evident port at the output of thematched receiver node 228 will flag corrupted photons, indicating acompromise of the link.

The quantum communications system 200 shown in FIG. 6 may use thespread-photon scheme and respective fixed first and second waveplates284, 288 that can be arranged as a plurality of waveplates at respectivetransmitter and receiver nodes 226, 228. The waveplates 284, 288 mayinclude a half waveplate (HWP) to operate at a fixed point at eachstage, such as shown in the polarization map indicated generally at 290in FIG. 7 and at the point labeled “D.” The conjugate receiver node 228as described allows Alice at the transmitter node 226 to set her atleast first waveplates 284 such that the polarization of the pulse canbe spread over the entire sphere corresponding at the polarization mapas shown in FIG. 7 . The quantum communications system 200 may work atthe equatorial section of the polarization map 290 or “globe” thatincludes the point “D” to not bias the power in any stage arm. Assuminga +/−5 degree tolerance to each waveplate's settings, the system 200 mayreasonably divide the circle into 36 points for 36 possible states for Nstages. Compared to the quantum communications system 20 described inFIG. 1 , this results in a

$\frac{36^{N}}{2^{N}} \approx 2^{4.12N}$

increase in complexity for an adversary running a brute forceanalog/computational attack.

Alice at the transmitter node 226 may choose any setting for herwaveplate 284, creating an arbitrary time-polarization superposition ofthe outgoing pulse. This can be done at every stage in the spread-photonpulse transmitter 40. Any measurement made mid-link may disturb thetime-polarization superposition (detectable by Bob at his receiver node228) and any eavesdropper that does not have the correct polarizationsettings key will not be able to decode the message, even if they have areceiver that is identical to Bob's receiver. At the receiver node 228,Bob sets his second waveplates 288 such that his receiver is conjugateto Alice's transmitter node 226 to decode the message.

Referring to the graph of FIG. 8 , the number of possible states versusthe number of stages is illustrated and shows a comparison with thequantum communications system 20 of FIG. 1 and the quantumcommunications system 200 of FIG. 6 that incorporates the waveplates284, 288 for altering polarization as described above. The system 200 ofFIG. 6 has a greater number of possible states than the system 20 ofFIG. 1 .

Referring now to FIG. 9 , a schematic block diagram of the quantumcommunications system 200 is shown in FIG. 9 to illustrate thewaveplates 284 at the transmitter node 226 corresponding to Alice andthe waveplates 288 as a half-waveplate (HWP) and full waveplate (WP) andlocation where error detection may occur at the receiver node 228 asBob. The transmitter node 224 shows the H path and V path and thereceiver node 228 shows the H path and V path, all of which arereferenced below in the description of operation. The receiver node 228may include error detection 229 and signal detection such as at opticaldetector circuit 256.

It is possible to write the states in the form |P,t

where P is the polarization state and t is the time where the pulse iscentered. First and second waveplate 284, 288 operators are written asÛ_(WP), where the waveplates operate as: (Û_(WP)⊗I_(t))|P,t

→|P,t

. If the assumption is made that these do not change the temporal state,the operator for the unbalanced Mach-Zehnder interferometer (UMZI) withPBSs is:

Û _(UMZI) =|H

H|⊗{circumflex over (β)}(t ₁)+|V

V|⊗{circumflex over (β)}(t ₂).

The operator {circumflex over (β)}(t) performs operationI_(pol)⊗{circumflex over (β)}(t)|P,t₀

→|P,t₀+t). There are assumptions and conventions:

-   -   |P,t        is shorthand for |P        ⊗|t        =|P        t        .    -   I_(s) is the identity matrix for the D.O.F.

Define {circumflex over (β)}(t ₁){circumflex over (β)}(t ₂)={circumflexover (β)}(t ₁ +t ₂).

Using standard Jones matrix formalism:

$\left. {{\left. {❘H} \right\rangle = \begin{pmatrix}1 \\0\end{pmatrix}},{❘V}} \right\rangle = {\begin{pmatrix}0 \\1\end{pmatrix}.}$

It is necessary to model the channels correctly in order to accuratelysimulate system dynamics. The final state may be written as:

|ψ_(f)

=Û _(receiver) Û _(channel) Û _(transmitter)|ψ_(i)

.

It is possible to assume that the input state can be written as:

|ψ_(i)

=|H,t=0

.

It is possible to assume that the channel is not birefringent: eachpolarization obtains a constant phase shift/loss. It is possible toeffectively ignore the channel effects in calculating the optimalreceiver node 228. To keep formalism compact, it is possible to suppressidentity matrix so that (Û_(WP)⊗I_(t))=Û_(WP) with the understandingthat the waveplates 284, 288 do not affect time.

It is possible to look at the evolution of a state through a singlefilter stage. It is possible to assume that the initial state is |H,t=0

, so the state out of the filter is:

|ψ_(out)

=Û _(UMZI) Û _(WP,TX) |H,t=0

=Û _(transmitter)|ψ_(i)

.

The state at the receiver node 228 from a single stage transmitter node226 is:

❘ψ_(out)⟩ = Û_(TX)❘ψ_(i)⟩ = Û_(UMZI)Û_(WP, TX)❘H, t = 0⟩ = [❘H⟩⟨H❘Û_(WP, TX) ⊗ β̂(t_(s)) + ❘V⟩⟨V❘Û_(WP, TX) ⊗ β̂(t_(l))]❘H, t = 0⟩❘ψ_(out)⟩=⟨H❘Û_(WP, TX)❘H⟩❘H, t_(s)⟩ + ⟨V❘Û_(WP, TX)❘H⟩❘V, t_(l)⟩.

It is possible to ignore loss where there are unitary operators, soideally:

Û _(ideal RX) =Û _(TX) ⁺ =Û _(WP) ⁺ |H

H|⊗{circumflex over (β)}(−t _(s))+Û _(WP) ⁺ |V

V|⊗{circumflex over (β)}(−t _(l)).

However, this would need the operator {circumflex over (β)}(−t), whichthe quantum communications system 200 cannot do physically. For thatreason, the quantum communications system 200 may use the same UMZI asthe transmitter node 226 with a bit flip so that each polarizationreceives that same time shift, effectively negating the UMZI:

Û _(RX) =Û _(WP,TX) ⁺ |H

H|⊗{circumflex over (β)}(t _(l))+Û _(WP,TX) ⁺ |V

V|⊗{circumflex over (β)}(t _(s)).

Using the receiver node 228 as shown as in the schematic of the quantumcommunications system 200 diagram in FIG. 9 , the effect of the UMZI is:

Û _(Actual RX) =Û _(WP,RX) |V

H|{circumflex over (β)}(t _(l))+Û _(WP,RX) |H

V|⊗{circumflex over (β)}(t _(s)).

The quantum communications system 200 may recover the effective idealreceiver node 228 by allowing Û_(WP,RX)=Û_(WP,TX) ⁺Û_(HWP)(45°), and asa result:

Û _(WP,TX) ⁺ Û _(HWP)(45°)|V

H|⊗{circumflex over (β)}(t _(l))+Û _(WP,TX) ⁺ Û _(HWP)(45°)|H

V|⊗{circumflex over (β)}(t _(s))=Û _(WP,TX) ⁺ |H

H|{circumflex over (β)}(t _(l))+Û _(WP,TX) ⁺ |V

V|⊗{circumflex over (β)}(t _(s)).

For a concrete example, the second waveplate 288 may be a HWP that couldbe either set to +/−2.25 degrees such as:

${\hat{U}}_{WP} = {{{\hat{U}}_{HWP}\left( {{\pm 22.5}{^\circ}} \right)} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {\pm 1} \\{\pm 1} & 1\end{pmatrix}}}$ and$\left. \left. {\left. {\left. {❘\psi_{out}} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {❘{H,t_{s}}} \right.}} \right\rangle \pm {❘{V,t_{l}}}} \right\rangle \right\rbrack.$

The paths may be labeled with s and 1 for long and short. Thepolarization and temporal degrees of freedom are now entangled. To makea match for this filter, it is possible to pass the state through ahalf-waveplate set to 45 degrees to flip H and V:

$\left. \left. {\left. {\left. \rightarrow{❘\psi_{out}} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {❘{V,t_{s}}} \right.}} \right\rangle \pm {❘{H,t_{l}}}} \right\rangle \right\rbrack.$

Passing this through an identical UMZI gives:

$\left. {\left. \left. {\left. {\left. \left. {\left. {\left. {❘\psi_{out}} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {❘{V,{t_{s} + t_{l}}}} \right.}} \right\rangle \pm {❘{H,{t_{l} + t_{s}}}}} \right\rangle \right\rbrack = {\frac{1}{\sqrt{2}}\left\lbrack {❘V} \right.}} \right\rangle \pm {❘H}} \right\rangle \right\rbrack{❘{t_{s} + t_{l}}}} \right\rangle.$

It is possible to use the previous results to calculateÛ_(WP,RX)=Û_(HWP) ⁺(±22.5°)Û_(HWP)(45°), and →|ψ_(f)

=|H

|t_(s)+t_(l)

, and thus assumes no error.

Alice as the transmitter node 226 and Bob as the receiver node 228 mayeach have their own waveplate 284,288 operators given byÛ_(wp,A),Û_(wp,B). The state received (just before Bob's final PSB, andignoring the channel) is:

Û _(WP,B) Û _(UMZI,B) Û _(HWP)(45°)Û _(UMZI,A) Û _(WP,A) |H,0

.

If Bob's receiver node 228 balances the interferometer such thatÛ_(UMZI,B)=Û_(UMZI,A), then the following applies:

[Û _(WP,B) |H

V|Û _(WP,A) +Û _(WP,B) |V

H|Û _(WP,A)]|H,t _(s) +t _(l)

.

It is possible to set Û_(WP,B)=Û_(WP,A) ⁺Û_(HWP)(45°). There are norestrictions on what the second waveplate 288 can be. Bob at hisreceiver node 228 can always undo it.

When there are N states at the transmitter node 226 and the receivernode 228, and arbitrary waveplates 284, 288, the receiver state is:

Û _(1,RX) . . . Û _(N,RX) Û _(HWP)(45°)Û _(N,TX) . . . Û _(1,TX) |H,0

.

The “N-th” (first stage of the receiver node 228) is:

Û _(N,RX) Û _(HWP)(45°)Û _(N,TX)=(Û _(WP,N,RX) |H

V|⊗{circumflex over (β)}(t _(s,N))+Û _(WP,N,RX) |V

H|⊗{circumflex over (β)}(t _(l,N)))(|H

H|Û _(WP,N,TX) and ⊗{circumflex over (β)}(t _(s,N))+|V

V|Û _(WP,N,RX)⊗{circumflex over (β)}(t _(s,N) +t _(l,N)))=(Û _(WP,N,RX)|H

(V|Û _(WP,N,TX) +Û _(WP,N,RX) |V

H|Û _(WP,N,TX))⊗{circumflex over (β)}(t _(s,N) +t _(l,N)).

It is possible to let Û_(WP,N,RX)=Û_(HWP)(45°)Û_(WP,N,tX) ⁺Û_(HWP)(45°).The first two terms may remove the effect of the Nth scrambling stage.The third term reflips the polarization for the next unscrambling stage.This process continues but with Û_(WP,1,RX)=Û_(WP,1,TX) ⁺Û_(HWP)(45°).Alice as the transmitter node 226 may choose each of the waveplates 284to be anything, but Bob as the receiver node 228 must know what each oneis. There are many possibilities, which may require securecommunications or prior knowledge.

Referring again to the graph of FIG. 8 , the quantum communicationssystem 200 shown in FIG. 6 that uses the first waveplate 284 to alterthe polarization state of the pulses is compared to the quantumcommunications system 20 shown in FIG. 1 , which does not incorporatethe waveplates but still spreads the photons such that its pulse divider42 divides each pulse having a plurality of X photons into a pluralityof Y time bins with Y>X. This graph illustrates the advantage where thenumber of possible states is compared with the number of stages, showingat about 10 stages. The quantum communications system 20 of FIG. 1 hasabout 10³ possible states, while the quantum communications system shownin FIG. 6 that uses the waveplates 284,288 has about 10¹⁵ possiblestates.

Referring now to FIG. 10 , there shown a flowchart illustrated generallyat 300 for a method of operating the quantum communications system 200of FIG. 6 . The process starts (Block 302) and the transmitter node 226is operated to generate quantum pulses in the pulse transmitter 240(Block 304). The polarization state of each pulse is altered using atleast one first waveplate (Block 306). The quantum pulses are divided atthe pulse divider 242 to divide each pulse (Block 308). The receivernode 228 is operated to recombine the quantum pulses at the pulserecombiner 254 (Block 310). The pulses are passed through at least onesecond waveplate 288 (Block 312). The recombined pulses are received ata pulse receiver 256 (Block 314). The process ends (Block 316).

This application is related to copending patent applications entitled,“QUANTUM COMMUNICATIONS SYSTEM HAVING PULSES DIVIDED INTO TIME BINS ANDASSOCIATED METHODS,” which is filed on the same date and by the sameassignee and inventors, the disclosure which is hereby incorporated byreference.

Many modifications and other embodiments of the invention will come tothe mind of one skilled in the art having the benefit of the teachingspresented in the foregoing descriptions and the associated drawings.Therefore, it is understood that the invention is not to be limited tothe specific embodiments disclosed, and that modifications andembodiments are intended to be included within the scope of the appendedclaims.

1. A quantum communications system comprising: a transmitter node, areceiver node, and a quantum communications channel coupling thetransmitter node and receiver node; the transmitter node comprising apulse transmitter, a pulse divider downstream from the pulsetransmitter, and at least one first waveplate upstream from the pulsedivider and configured to alter a polarization state of pulsestravelling therethrough; the receiver node comprising at least onesecond waveplate being a conjugate of the at least one first waveplate,a pulse recombiner upstream from the at least one second waveplate, anda pulse receiver downstream from the at least one second waveplate. 2.The quantum communications system of claim 1 wherein the pulse divideris configured to divide each pulse having a plurality of X photons intoa plurality of Y time bins with Y>X.
 3. The quantum communicationssystem of claim 1 wherein the pulse receiver comprises at least onesingle photon detector.
 4. The quantum communications system of claim 1wherein the pulse divider comprises a plurality of staged birefringentcrystals.
 5. The quantum communications system of claim 1 wherein thepulse recombiner comprises a plurality of staged birefringent crystals.6. The quantum communications system of claim 1 wherein the pulsetransmitter is configured to generate temporally modulated photons. 7.The quantum communications system of claim 1 wherein the quantumcommunications channel comprises at least one of a fiber opticcommunications channel, a free space optic communications channel, andan underwater optic communications channel.
 8. The quantumcommunications system of claim 1 wherein the pulse transmitter isconfigured to generate orthogonally modulated photons.
 9. The quantumcommunications system of claim 1 wherein the pulse transmitter isconfigured to generate a bit stream of quantum pulses in a quantum keydistribution (QKD) protocol.
 10. A quantum communications systemcomprising: a communications system; and a quantum key distribution(QKD) system operable with the communications system and comprising thetransmitter node comprising a pulse transmitter, a pulse dividerdownstream from the pulse transmitter, and at least one first waveplateupstream from the pulse divider and configured to alter a polarizationstate of pulses travelling therethrough; the receiver node comprising atleast one second waveplate being a conjugate of the at least one firstwaveplate, a pulse recombiner upstream from the at least one secondwaveplate, and a pulse receiver downstream from the at least one secondwaveplate.
 11. The quantum communications system of claim 10 wherein thepulse divider is configured to divide each pulse having a plurality of Xphotons into a plurality of Y time bins with Y>X.
 12. The quantumcommunications system of claim 10 wherein the pulse receiver comprisesat least one single photon detector.
 13. The quantum communicationssystem of claim 10 wherein the pulse divider comprises a first pluralityof staged birefringent crystals; and wherein the pulse recombinercomprises a second plurality of staged birefringent crystals.
 14. Thequantum communications system of claim 10 wherein the pulse transmitteris configured to generate temporally modulated photons.
 15. The quantumcommunications system of claim 10 wherein the quantum communicationschannel comprises at least one of a fiber optic communications channel,a free space optic communications channel, and an underwater opticcommunications channel.
 16. The quantum communications system of claim10 wherein the pulse transmitter is configured to generate orthogonallymodulated photons.
 17. The quantum communications system of claim 10wherein the pulse transmitter is configured to generate a bit stream ofquantum pulses in a quantum key distribution (QKD) protocol.
 18. Amethod of operating a quantum communications system comprising atransmitter node, a receiver node, and a quantum communications channelcoupling the transmitter node and receiver node, the method comprising:operating the transmitter node to generate quantum pulses at a pulsetransmitter and dividing the quantum pulses at a pulse divider, thetransmitter node also comprising at least one first waveplate upstreamfrom the pulse divider to alter a polarization state of pulsestravelling therethrough; operating the receiver node to recombine thedivided quantum pulses at a pulse recombiner, and receiving therecombined pulses at a pulse receiver, the receiver node also comprisingat least one second waveplate downstream of the pulse recombiner andbeing a conjugate of the at least one first waveplate.
 19. The method ofclaim 18 wherein the pulse divider divides each pulse having a pluralityof X photons into a plurality of Y time bins with Y>X.
 20. The method ofclaim 18 wherein the pulse receiver comprises at least one single photondetector.
 21. The method of claim 18 wherein the pulse divider comprisesa first plurality of staged birefringent crystals, and wherein the pulserecombiner comprises a second plurality of staged birefringent crystals.22. The method of claim 18 wherein the quantum communications channelcomprises at least one of a fiber optic communications channel, a freespace optic communications channel, and an underwater opticcommunications channel.
 23. The method of claim 18 wherein the pulsetransmitter is configured to generate orthogonally modulated photons.24. The method of claim 18 wherein the pulse transmitter is configuredto generate a bit stream of quantum pulses in a quantum key distribution(QKD) protocol.